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Galilean Invariance and Mach’s Principle

Frederick David Tombe,

Northern Ireland, United Kingdom,

sirius184@hotmail.com

10th April 2014

Abstract. Galileo’s “Principle of Relativity” omits any consideration of an absolute frame

of reference with respect to which motion is measured. Kinetic energy would appear to

be a relative quantity whose magnitude depends on the chosen frame of reference, or in

the case of its centrifugal force derivative, depends on which polar origin is chosen. The

magnitude of any physical interaction involving two bodies is only ever dependent on

their relative velocity, and there seems to be no way of exposing the existence of any

special frame of reference with respect to which linear kinetic energy is an absolute

physical quantity. The fact of centrifugal force however does indicate that such a frame

of reference must exist, and that this frame appears to be embedded in a medium that is

in a state of zero rotation relative to the fixed background stars. Rotation relative to the

fixed background stars induces centrifugal force, which suggests that kinetic energy is

indeed an absolute physical quantity that is induced by the interaction of a moving body

with a physical medium which pervades all of space.

In this article it will be proposed that the physical medium for the propagation of

light is also the cause of kinetic energy and centrifugal force, and we will be reminded

that Maxwell’s equations are formulated specifically with this medium as the standard

of rest. Important questions relating to the motion of this luminiferous medium relative

to the planets and the stars will then be discussed.

The Aether

I. It is proposed that space is densely packed with tiny aethereal whirlpools that

are pressing against each other with centrifugal force while striving to dilate [1],

[2], [3], [4]. Gravity and electric current consist in the flow of this aether, with the

flow momentum normally denoted either by the vector A or J according to the

context. It is most important however to make a distinction between the pure

aether itself, on the one hand, and the sea of tiny aethereal whirlpools which

constitutes the luminiferous medium for the propagation of light, on the other

hand. Kinetic energy and centrifugal force on the large scale are induced when a

body moves through the background luminiferous medium. The induction

follows from the shear interaction which causes an angular acceleration of the

tiny aethereal whirlpools. The induced angular acceleration in these tiny

whirlpools causes an increase in the centrifugal pressure surrounding the

moving body, while electromagnetic radiation constitutes a propagation of such

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fine-grained angular acceleration through the luminiferous medium. Hence the

medium that is the cause of kinetic energy and centrifugal force is also the

medium that is the cause of electromagnetic phenomena and which acts as the

carrier of electromagnetic waves. The phenomenon of linear kinetic energy can

never be measured absolutely and neither does it provide any basis upon which

we can detect the existence and relative motion of the luminiferous medium. In

the case of two bodies in relative motion, kinetic energy can only be physically

experienced when the two bodies come into contact with each other, and when

this occurs, the magnitude of the physical reaction depends entirely on their

relative velocities. The laws of linear classical mechanics are said to be

“Galilean Invariant”.

The absence of the luminiferous medium in modern physics does not

impact upon linear classical mechanics, but it does create a serious deficiency in

both rotational classical mechanics and electromagnetism. Galileo’s “Principle

of Relativity” was good for linear motion, which is all that he intended it for,

and the law of vector addition of velocities which stems from it still holds good

even when we introduce the luminiferous medium. The manner in which

Einstein later confused matters, due to his inability to comprehend Maxwell’s

equations, should not on any account be blamed on Galileo.

Electromagnetic Induction and Galilean Invariance

II. When a moving magnet induces an EMF in a coil, it makes no difference

whether we move the magnet into the coil or move the coil over the magnet.

The energy comes from the relative motion, and the situation is parallel to that

of a collision in classical mechanics. In both cases the input energy is linear

kinetic energy. It would seem therefore that Galilean invariance applies to

convective electromagnetic induction. There are however further issues that will

be discussed in section IV below.

Rotational Motion

III. Rotational motion in classical mechanics does expose the existence of the

luminiferous medium by virtue of the induction of centrifugal force when the

rotation is measured relative to the fixed background stars. Centrifugal force is

the radial derivative of kinetic energy relative to an arbitrarily chosen polar

origin, and so just like linear kinetic energy it is a relative quantity which is

realized during a mutual physical interaction. In the case of spinning bodies of

finite size, the centrifugal force is induced by the interaction with the

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luminiferous medium and in opposition to the intermolecular bonding forces

within the spinning body. We therefore conclude that the rotation of a body

does not cause the luminiferous medium contained within it to co-rotate, and

that the luminiferous medium moves freely through the interstitial spaces

between the atoms and the molecules, just like water flows through a basket.

Maxwell’s EMF Equation

IV. Maxwell’s electromagnetic force equation first appeared in his 1861 paper

“On Physical Lines of Force” [5] as equation (77),

E = μv×H − ∂A/∂t – gradψ (77)

and it is nowadays wrongly named the Lorentz force equation. Equation (77)

also appeared as equation (D) of the original eight Maxwell’s equations listed in

his 1864 paper “A Dynamical Theory of the Electromagnetic Field” [6], [7].

Maxwell physically explained the convective term μv×H on the right hand side

of equation (77) on the basis of compound centrifugal force. In other words, it’s

a Coriolis force of sorts with the velocity v being measured relative to the

luminiferous medium. The symmetry inherent in convective electromagnetic

induction described in section II above, suggests that we must be dealing with

the convective μv×H term irrespective of whether we consider the magnet to

have moved relative to the coil, or whether we consider the coil to have moved

relative to the magnet, and as such we deduce that a magnet in linear motion

must entrain a region of luminiferous medium within its magnetic field.

Centrifugal force is a convective effect, which on one scale or another, is

involved in all of the kinetic energy interactions mentioned in the sections

above. Even though an object that is made of atomic and/or molecular matter

experiences centrifugal force when it rotates, it does not however radiate

centrifugal force. This can be demonstrated by the absence of mutual repulsion

between two spinning gyroscopes in close proximity, or by the fact that a

magnet which is rotating on its magnetic axis does not induce an EMF at a

distance. When however a magnet is rotating other than about its magnetic axis,

it does induce an EMF at a distance. The important difference here is that we

are now dealing with precession of the magnetic axis and hence angular

acceleration of the tiny aethereal whirlpools that make up the magnetic field.

We are dealing with a unidirectional propagation of rotational, or more

precisely of precessional kinetic energy, and there is no symmetry as like in the

linear convective case described in section II above. Just as in the case of the

transverse planetary orbital equation, Maxwell’s EMF equation has both a

Coriolis term and an angular acceleration term. The angular acceleration,

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−∂A/∂t, is the second term in equation (77) above. This is the basis of time

varying electromagnetic induction and electromagnetic radiation, both of which

are in fact a propagation of angular acceleration, and hence a propagation of

fine-grained centrifugal force through the luminiferous medium. Of the three

EMF terms on the right hand side of equation (77), Maxwell only used the zero

divergence −∂A/∂t term when deriving the electromagnetic wave equation. The

remaining term, –gradψ, is Gauss’s law which can apply to gravity, magnetic

attraction, or to electrostatic attraction, but like μv×H, it is not involved in the

derivation of the electromagnetic wave equation.

Maxwell was working on the basis that his equations apply in the rest frame

of the luminiferous medium. The speed of light would therefore be measured

relative to that medium. When observed from any frame of reference that is in

motion relative to the luminiferous medium, the speed of light would simply be

measured as per Galilean vector addition of velocities. Einstein wrongly

preached that Maxwell’s equations are independent of any particular frame of

reference and that hence the speed of light would always be observed to have

the same value no matter from which frame of reference it is observed. Einstein

had absolutely no basis upon which to draw this absurd conclusion and it is his

abandoning of Galilean vector addition of velocities in relation to the speed of

light that lies at the cornerstone of his special theory of relativity, and as such it

is fair to state that on this basis alone Einstein’s theories of relativity are

completely and totally false.

Because of the unnecessary confusion caused by Einstein, opponents of

Einstein often get bogged down in unnecessary arguments surrounding whether

or not Maxwell’s equations can be said to be Galilean invariant as is the case

with linear classical mechanics. While the speed of light obeys Galilean vector

addition of velocities, the equations themselves are formulated specifically in

the rest frame of the luminiferous medium, and as such are not technically

Galilean invariant. There is of course never any need to subject Maxwell’s

equations to a coordinate frame transformation, and so the subject of Galilean

invariance in connection with Maxwell’s equations is merely irrelevant

semantics. It’s much more important that we accurately ascertain the relative

motion of the luminiferous medium with respect to the Earth and the wider

universe.

Those who don’t believe in the existence of a physical medium for the

propagation of light will of course remain eternally confused when it comes to

the issue of Maxwell’s equations, frames of reference, and what the v in μv×H

is measured relative to. Their punishment will be to spend their days struggling

to make sense out of that of which no sense can be made. They will find

themselves immersed in endless debates, wrangling over the meaning of

meaningless terms like Lorentz invariance and even Lorentz covariance! These

are big words which sound scientific, but when scrutinized closely are found to

lack any substantial meaning in the real world. Sadly however, even amongst

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those who still believe in the luminiferous medium, many have nevertheless

been dragged down into that mad world of Lorentz transformations and its

many variants, due to another absurd belief, and the absurd belief in question is

another of Lorentz’s gems. It is the foolish belief that the Michelson-Morley

null result is explained away by a physical contraction of the apparatus caused

by an aether wind that just happens to exactly to cancel with the sought after

effect.

The Rest Frame of the Luminiferous Medium

V. Maxwell’s equations arose out of terrestrial laboratory experiments and they

corroborated with the directly measured speed of light. The question then

remained as to what is the relative velocity of the luminiferous medium and the

Earth? The Michelson-Morley experiment of 1887created a controversy over

this question, and to this day that controversy has never been resolved.

In the case of the Earth’s orbital motion about the Sun, the Earth’s magnetic

field will entrain a region of luminiferous medium, and the Earth’s gravitational

field will augment this drag effect and extend the entrained region well beyond

the magnetosphere. There will therefore be no relative motion of the Earth and

the luminiferous medium due to the Earth’s orbital motion. If this were not the

case, the Michelson-Morley experiment of 1887 would have shown up

significant interference fringes relating to the orbital speed of 30km/sec.

Entrainment is the only viable conclusion short of entering into the absurd

world of Lorentz contractions and transformations. Lorentz objected to Stokes’

perfectly rational aether drag approach on premature grounds. One of his

objections was that entrainment would result in vortices at the interface where

the entrainment terminated. That however is not a valid objection since we do

indeed have vortices at the interface and they are necessary for the production of

orbital centrifugal force. Rather than cause friction that would in turn cause the

planets to spiral into the Sun, the luminiferous medium in fact causes the very

inertial forces that prevent this from happening.

As regards the Earth’s diurnal rotation, the 1925 Michelson-Gale

experiment seems to suggest that the luminiferous medium does no co-rotate.

This would be further borne out by Coriolis and centrifugal effects in the

atmosphere and also by effects such as that observed with a Foucault pendulum

which are dependent on the luminiferous medium not co-rotating with the Earth.

These inertial effects may also however be augmented to a greater or lesser

degree by the electromagnetic force F = qv×B arising from the Earth’s magnetic

field, where q derives from the fact that all atomic and molecular matter has a

mild negative electric charge.

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Mach’s Principle

VI. Unlike in the case of linear motion which does not expose an absolute frame

of reference, rotational motion, specifically with reference to the fixed

background stars, induces centrifugal force. This often raises the question as to

whether or not there is some kind of physical interaction with the background

stars. The background stars of course are not actually fixed. They are all in

relative motion to each other, but their instantaneous position seems to define a

distinct frame of reference that possesses a physical reality with respect to

rotation.

Centrifugal force however will almost certainly be generated locally due to

interaction with the luminiferous medium, but the rest frame of this medium, at

least from a rotational perspective, will be in turn determined by the average

position of the background stars. So in answer to the often asked question as to

whether or not the background stars play a role in local rotations, the answer is

that they do, but only indirectly.

Conclusion

VII. Mainstream physics preaches that light propagates in pure vacuum. This is

an absurd twentieth century notion which is rejected by many, but amongst

those who do believe in the existence of a physically real luminiferous medium,

there are many side arguments. First of all there is the issue of whether the

luminiferous medium is one and the same medium as the aether that is the cause

of gravity. Secondly there is the issue of the relative motion of the luminiferous

medium with respect to the background stars and the planetary bodies. The

conclusion of this paper is that while the luminiferous medium does account for

the inertial forces, it is not the same thing as the gravitational aether. The

luminiferous medium is a dense sea of tiny aether whirlpools while gravity

arises due to a large scale flow of aether through the luminiferous medium. The

tiny aethereal vortices of the luminiferous medium absorb large scale vorticity

from the gravitational aether flow, meaning that the gravitational aether and the

luminiferous medium are very closely interconnected. It is the same aether, but

it is very important to distinguish between the two distinct concepts.

The luminiferous medium is attracted by the Earth’s gravity, but the fine-

grained centrifugal pressure within it prevents it from being pulled into the

Earth. The combined effect of the Earth’s gravitational field and the Earth’s

magnetic field ensures that the luminiferous medium within the gravitational

field moves with the Earth in the Earth’s orbital motion around the Sun. The

gravitational aether meanwhile flows radially downwards into the Earth,

through the luminiferous medium. The issue of whether or not the luminiferous

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medium co-rotates with the Earth’s rotation is not so easy to determine

precisely, but most of the evidence tends to suggest that the luminiferous

medium does not co-rotate with the Earth’s rotation.

Since light is aethereal, the path of light will be affected by the downward

flow of aether that is the cause of gravity. However, since EM radiation is a

propagation of fine-grained centrifugal force moving through the luminiferous

medium, the degree of bending will not be lessened by the centrifugal force that

keeps the planets in their orbits. We have no way of accurately calculating the

degree of light bending by gravity.

References

[1] O’Neill, John J., “PRODIGAL GENIUS, Biography of Nikola Tesla”, Long Island, New York, 15th July

1944

“Long ago he (mankind) recognized that all perceptible matter comes from a primary substance, of a tenuity

beyond conception and filling all space - the Akasha or luminiferous ether - which is acted upon by the life-

giving Prana or creative force, calling into existence, in never ending cycles, all things and phenomena. The

primary substance, thrown into infinitesimal whirls of prodigious velocity, becomes gross matter; the force

subsiding, the motion ceases and matter disappears, reverting to the primary substance”

http://www.rastko.rs/istorija/tesla/oniell-tesla.html

[2] Whittaker, E.T., “A History of the Theories of Aether and Electricity”, Chapter 4, pages 100-102, (1910)

“All space, according to the younger Bernoulli, is permeated by a fluid aether, containing an immense number

of excessively small whirlpools. The elasticity which the aether appears to possess, and in virtue of which it is

able to transmit vibrations, is really due to the presence of these whirlpools; for, owing to centrifugal force,

each whirlpool is continually striving to dilate, and so presses against the neighbouring whirlpools.”

[3] Lodge, Sir Oliver, “Ether (in physics)”, Encyclopaedia Britannica,

Fourteenth Edition, Volume 8, Pages 751-755, (1937)

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in a state of fine-grained vortex motion, circulating with that same enormous speed. For it has been partly,

though as yet incompletely, shown that such a vortex fluid would transmit waves of the same general nature as

light waves— i.e., periodic disturbances across the line of propagation—and would transmit them at a rate of

the same order of magnitude as the vortex or circulation speed”

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[5] Clerk-Maxwell, J., “On Physical Lines of Force”, Philosophical

Magazine, Volume XXI, Fourth Series, London, (1861)

http://vacuum-physics.com/Maxwell/maxwell_oplf.pdf

[6] Clerk-Maxwell, J., “A Dynamical Theory of the Electromagnetic

Field”, Philosophical Transactions of the Royal Society, 155, pp 459-512 (1865). Abstract: Proceedings of the

Royal Society of London 13, pp. 531--536 (1864)

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